Investigation into the relationship between acceleration and the angle of free fall downhill

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Investigation into the relationship between acceleration and the angle of free fall downhill


This is an investigation into the free fall of an object (in this case a small cart/trolley). When an object is placed on an inclined plane, the object is most likely to fall through the plane. Moreover, when the height of the plane is increased it was found that the object took less time to get to the other end. I decided to investigate the relationship between the angle of the slope of the plane and the acceleration of the object.


To investigate the extent of which the angle of the slope of the inclined plane is related to the acceleration of the object as it goes through the plane.

Independent Variables

Angle of the slope of the wooden ramp

Dependent Variables

Acceleration of the object

Controlled Variables

  • Length of the plane
  • Height of the plane
  • Initial velocity of the object (= 0 ms-1)
  • Distance travelled by the object


The sine of the angle of the slope will be directly proportional to the acceleration of the object.


Where a is acceleration, θ is the angle of the slope, v is the final velocity, u is the initial velocity and t is time. For the second formula g is acceleration due to gravity (≈9.81 m s-2).


  • Wooden Ramp
  • 1 Meter Ruler
  • Stopwatch
  • Bricks
  • Books
  • Dynamics Cart

Method of Data Collection


  1. A brick was set under one of the wooden ramp’s ends, leaving the other end touching the ground. The length (adjacent side to the angle) was measured with a ruler and was then recorded, which would be 59.8 cm for all trials.
  2. Another brick was set in front of the other end of the wooden ramp. At the same time, the height of the plane was recorded, noting that the ramp already had a height of 2 cm. This value was then subtracted from the total height, to obtain the original height, which was then recorded
  3. The cart was positioned at the starting point in rest, and was then released. The time was recorded with a stopwatch from the moment the cart was released to the moment it hit the brick.
  4. Step 3 was repeated with 5 different heights: 8.4, 11.8, 13.4, 15.2, and 17.6 cm (later changed to meters for data analysis). These heights were used instead integers because it was the height of the brick and books used.
  5. For all the different heights (Step 4) there were 5 trials, all results were recorded to be further processed.  

Measuring the dependant and independent variables:

The acceleration of the cart when it goes downhill (dependant variable) was calculated from the measuring of the time taken for the cart to go downhill. To get more accurate results, the help of a partner was needed; the moment when the cart hit the brick thus ending its trajectory would be better appreciated. The independent variable (angle of the slope) was calculated from the measuring of the height and length of the plane. This was done with a 1 meter ruler, which was placed parallel to the ramp to avoid any errors.

Controlling the controlled variables:

The angle of the slope was determined from the length and height of the plane; therefore it could be controlled as the length and height changed. The length was measured from the starting point to the ending point of the distance travelled by the cart when it went downhill. The starting point wouldn’t be touching the ground therefore it was harder to get an exact result; to control this, the brick was positioned under the starting point and it was assumed that the height measured was in a 90° angle with both the starting point mark and the surface. The point where the brick made contact with the ground was marked and so it was easier to measure the length. The height was then measured from the starting point to the point where the brick is in contact with the ground. This result was then subtracted 2 cm because that was the height of the ramp, meaning that when the object got to the ending point it would still be 2 cm above the ground.

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The distance travelled by the object was controlled at all times by putting a mark on the starting point, this way the object would never start over the starting point and would always cover the same distance. The initial velocity of the object was always kept at 0; a partner would make sure the object wasn’t moving before being released.  The help of a partner was essential; otherwise it was too hard to concentrate on both controlling the initial velocity and measuring the time.


Raw data

The Table below shows the time ...

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